11x11 Queens Puzzle #168

Difficulty: easy. Place 11 queens on this 11x11 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 13-step reasoning is written out below.

Previous puzzle · All 11x11 puzzles · Next puzzle

Step-by-step solution for puzzle #168

What follows is a complete solve of puzzle #168, worked the way a person works it rather than the way a computer does. It runs to 13 deductions — 11 queen placements and 2 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region confined to one line.

Techniques this board needs: last square in a region, region confined to one line.

Show the full walkthrough (6 steps) — contains the solution

  1. Step 1. Only row 1, column 11 is still open in indigo, and since each colour must take a queen, that settles it. That clears row 1, column 11, the rest of the indigo region and every square adjacent to it — diagonals included.

  2. Step 2. The orange region is down to one open square, at row 9, column 1. Every colour holds exactly one queen, so that square is forced. Cross out the whole of row 9 and column 1, the remaining orange squares, and the ring of neighbours around row 9, column 1.

  3. Step 3. Only row 11, column 6 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 6, in teal and in the ring around that square is now dead.

    Puzzle #168 after step 3: 3 of 11 queens placed
    The board after step 3 — 3 of 11 queens placed.

  4. Step 4. All of the blue region's remaining squares (2 open squares) lie in column 10. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.

  5. Step 5. Slate cannot leave column 3 — every one of its open squares (2 open squares) sits there. That column belongs to slate, so every square in it owned by another colour is dead: 10 squares in all.

  6. Step 6. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: pale yellow has one square left, so its queen takes row 7, column 2; slate has one square left, so its queen takes row 5, column 3; blue has one square left, so its queen takes row 3, column 10; amber has one square left, so its queen takes row 2, column 4; red has one square left, so its queen takes row 6, column 9; khaki has one square left, so its queen takes row 8, column 5; sea green has one square left, so its queen takes row 10, column 8; mint has one square left, so its queen takes row 4, column 7. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 4, column 7.

    Puzzle #168 after step 6: 11 of 11 queens placed
    The board after step 6 — 11 of 11 queens placed.

That completes the board: 11 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.

About 11x11 Queens puzzle #168

This is puzzle number 168 in the 11x11 collection, rated easy. The grid holds 121 squares split between eleven colored regions, and a finished board carries eleven queens — one in every row, one in every column, one in every color, and never two of them touching, diagonals included.

Puzzle #168 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.

How the colors divide this board

From smallest to largest, the regions on puzzle #168 are: indigo (1 square), orange (1 square), teal (1 square), slate (2 squares), blue (9 squares), red (9 squares), pale yellow (9 squares), mint (16 squares), amber (22 squares), khaki (23 squares), sea green (28 squares). An even split would hand every color 11 squares, so the indigo region is running 10 squares under that average while the sea green region is the roomiest area on the grid with 28 squares.

One queen per color, regardless of acreage: that is what turns this uneven split into a solving order. Indigo is working with 1 square while sea green has 28 to spare, a gap of 27. Attack the cramped end and the roomy regions tend to resolve themselves.

Shape matters as much as size. The indigo region is the most compact color here, filling 100% of the 1×1 box that encloses it, while mint is the most scattered at 44% of its 6×6 box. Compact regions are easy to eliminate around; straggling ones reach into more rows and columns and tend to stay unresolved until late.

Region by region

Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a easy board.

Indigo: 1 square across rows 1–1, columns 11–11. It never leaves row 1, so its queen is locked to that row.

Orange covers 1 square, spanning 1 row and 1 column (rows 9–9, columns 1–1). It never leaves row 9, so its queen is locked to that row.

Teal occupies 1 square within rows 11–11, columns 6–6. It never leaves row 11, so its queen is locked to that row.

Slate: 2 squares across rows 5–6, columns 3–3. It sits wholly inside column 3, so its queen must be in that column.

Blue covers 9 squares, spanning 5 rows and 3 columns (rows 1–5, columns 9–11).

Red occupies 9 squares within rows 4–7, columns 7–10.

Pale yellow: 9 squares across rows 5–8, columns 1–3.

Mint covers 16 squares, spanning 6 rows and 6 columns (rows 1–6, columns 4–9).

Amber occupies 22 squares within rows 1–4, columns 1–7.

Khaki: 23 squares across rows 6–11, columns 1–7.

Sea green covers 28 squares, spanning 6 rows and 6 columns (rows 6–11, columns 6–11).

Where to start on this board

Open on the tightest color. Here that is indigo, confined to 1 square between rows 1 and 1 and columns 11 and 11. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #168.

Because indigo never leaves row 1, its queen must be in that row — and that instantly settles row 1 for everyone else. Sweep along it and X out every square that is not indigo. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.

Work outward to the other flat regions next. Orange, teal and slate are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.

The tightest lines on puzzle #168

A quick way to find the next move is to count how many different colors touch each line. On this board, row 10 is the narrowest, touched by only 2 colors. Columns 2, 4, 5, 8, 10 and 11 are the tightest columns, with 3 colors.

Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 2 colors, then one of those regions has to own it, and every other region is competing for the remaining 10 rows. By contrast row 6 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.

Working through the middle game

The middle of #168 is where careless play costs time. Every queen you place kills a row, a column and the eight surrounding squares; if you do not mark all of that immediately, you will later "discover" a move that was available several turns ago. Mark first, then look.

With eleven queens to seat and eleven regions competing over 121 squares, keep two questions in rotation. Does any region now have exactly one open square left? That queen is forced. Does any row or column now have exactly one open square left? That queen is forced too. Alternating between the region view and the row-and-column view is what keeps a solve moving, and it is the clearest difference between players who finish 11x11 boards quickly and players who stall halfway.

Say the reason out loud: "this region has one square left", "this column has one square left". If no such sentence is available, the eliminating is not finished. One more pass of X marks is almost always quicker than committing to a placement you cannot defend.

Why puzzle #168 is rated easy

The easy label comes out of four measurable things about #168: seven of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 2 colors, and its largest and smallest regions differ by 27. Boards that score tight on those measures give up their first queen fast.

Rating is a measure of chain length, not of chance. With one guaranteed solution and no guessing required, the only thing that changes across the collection is how many eliminations you must link together before a queen is provably forced.

When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.

Techniques that work well at 11x11

At 11x11 you are managing 121 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.

Whatever the grid size, the pairing rule is the technique to internalise. When a pair of regions is boxed into the same pair of rows, they split those rows between them and nobody else may enter — and the same holds for columns, or for any n regions confined to n lines. Look for an instance of it around row 10 on this board.

As a sanity check rather than a spoiler: the finished solution to #168 puts 3 queens on the outer border and 8 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.

How to play Queens

  1. The board is an N×N grid divided into N colored regions.
  2. Place exactly one queen (♛) in each row, each column, and each colored region.
  3. No two queens may touch each other — not horizontally, vertically, or diagonally.
  4. Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
  5. There is always exactly one valid solution. Use logic, never guessing, to find it.

Full rules · Strategy library · Puzzle statistics

Questions about this puzzle

How hard is 11x11 Queens puzzle #168?

Puzzle #168 is rated easy. Its smallest color region holds 1 square, its tightest row is touched by 2 colors, and seven of its regions are confined to a single row or column, which gives you a forced move early.

Does 11x11 puzzle #168 have only one solution?

Yes. Every puzzle in the 11x11 collection, including #168, has been verified to have exactly one valid arrangement of eleven queens, and it can always be reached by logic alone — no guessing or backtracking needed.

Where should I place my first queen on puzzle #168?

Start with the indigo region — the most constrained color on this board, with 1 square spanning rows 1–1 and columns 11–11. Narrowing the smallest region first removes the most squares elsewhere on the grid.